In a study to examine the relationship between the time required to complete a c

Question

In a study to examine the relationship between the time required to complete a construction project and several pertinent independent variables, an analyst compiled a list of four variables that might be useful in predicting the time to completion. These four variables were size of the contract, X1 (in $1000 units), number of workdays adversely affected ty the weather X2, a variable X3 that indicates the presence (X3 = 1) or absence (X3 = 0) of a workers’ strike and number of subcontractors involved in the project X4. Fifteen construction projects were randomly chosen and each of the four variables as well as the time to completion were measured.

The SAS output is given here and then you are to answer the questions below using this SAS output only and no rounding is allowed.

Linear Regression Results: End of Chapter 4 Assessment

The REG Procedure
Model: Linear_Regression_Model
Dependent Variable: Y

CHAPTER 4.2 ASSESSMENT

1. Using the material above, please select the correct answer for each item.

Y X1 X2 X3 X4 29 60 7 0 7 15 80 10 0 8 60 100 8 1 10 10 50 14 0 5 70 200 12 1 11 15 50 4 0 3 75 500 15 1 12 30 75 5 0 6 45 750 10 0 10 90 1200 20 1 12 7 70 5 0 3 21 80 3 0 6 28 300 8 0 8 50 2600 14 1 13 30 110 7 0 4

Explanation / Answer

All the information are filled using the SAS output table:

1)R-squared= 0.8471 [OPTION A]

2) SSE= 1403.03618 (Using the Analysis of variance table) [OPTION B]

3)S-Squared= Now we know that S-squared is an unbaised estimator of sigma-square(The error variance)

Now we know that sigma-hat-squared= MSE= SSE/ df = 140.30362

Hence S-squared= 140.30362 [OPTION C]

4) S= square root(S-squared)= 11.84498 [OPTION D]

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